The mechanism of boundary lubrication and the properties of the lubricating film

THE MECHANISM OF B O U N D A R Y LUBRICAT[ON AND THE PROPERTIES. OF THE LUBRICATING FILM SHORT-

AND

LONG-RANGE BOUNDARY

ACTION

IN

THE

THEORY

OF

LUBRICATION

B. V. D E R Y A G U I N C o r r e s p o n d i n g M e m b e r of the A c a d e m y of Sciences of U.S.S.R. in c o l l a b o r a t i o n with V. V. K A R A S S E V , N. N. Z A K H A V A E V A

A N D V. P. I . A Z A R E V

Laboratory of Sur[ace Phenomena, Institute of Physical Chemistry, Academy of Sciences of U.S.S.R., Moscow (U.S.S.R.)

SUMMA R Y T w o versions of the blow-off m e t h o d are described, by m e a n s of w h i c h the d e p e n d e n c e of the viscosity of oils and o t h e r n o n - v o l a t i l e fluids o n t h e d i s t a n c e f r o m the solid wall can be measured. a n d the viscosity localized w i t h a n a c c u r a c y of ~o ]k. In the case of n o n - p o l a r s p e c i a l l y purified vaseline oil the v i s c o s i t y r e m a i n s s t r i c t l y c o n s t a n t to a d i s t a n c e of the order of ~o -v c m from the wall. The a d d i t i n n ~f p~lar a d d i t i v e s c a u s e s changes in the viscosity near the wall. I n a n u m b e r of cases the viscosity c h a n g e s d i s c o n t i n u o u s l y at s o m e d i s t a n c e s of the order of lo -G t~ lo -~ c m from the wall. In tile case of p o l a r liquids the viscosity m a y rise o r iall on a p p r o a c h i n g thc wall. d e p e n d i n g on the m o l e c u l a r s t r u c t u r e The r e s u l t s o b t a i n e d prove t h a t the ~,olid wall is c a p a b l e ~,f a l t e r i n g the o r i e n t a t i o n of the molecules in a d j a c e n t layers of the liquid u p ' t o Io -s cm thick, and e v e n u p to lo -'~ cm thick in the case of p o l y m e r i c liquids. This effect p l a y s a s u b s t a n t i a l l)aTt in tile mechanisn~ of b o u n d a r y lubrication. since oiliness a l w a y s d i s a p p e a r s if it is a b s e n t . In conclusion, an e x a m i n a t i o n is m a d e of the m e c h a m c a l propel ties of the b o u n d a r y lubrication layer w h i c h explain b o t h the e x i s t e n c e ofs]zattc f r i c t m n and the ¢~bservation ,_,f the t w o - t e r m friction law d e r i v e d b y DERV.~CUI~ f r o m the m o l e c u l a r theory, of f r i c t m n The general conclusion is t h e i m p o s s i b i l i t y of a c c o u n t i n g f~Jr the p h e n o m e m m of b o u n d a r s ' l u b r i c a t i o n w i t h o u t t a k i n g into c o n s i d e r a t i o n tim specific prr, t~crl its ~,f the i m t y m o l e c u l a r b o u n d a r y layers of liquids.

Z U S A M ,1,I E .\ F.-I 5S ( ~.kG

Zwei verschiedene V a r i a n t e n der s o g e n a n n t e n A b b l a s - n l c t h o d e w e r d e n beschrieben, l)iesc erl a u b e n es die Abh~.ngigkeit d e r Z/ihigkeit yon Olen u n d a n d e r e n nicht-fliichtigcn [:liissigkeiten als F u n k t i o n des A b s t a n d e s ,'on d e r festen \.\:and zu mcssen und dic Z/ihigkeil mit ci,,er Genauigkeit bis a u f I o ]k zu lokalisieren. Fiir ein n i c h t p o l a r e s speziell gereinigtes Vaselin61 bleiht d,e Z;ihigkeit s t r e n g .atabil his zu einem A b s t a n d y o n der W a n d y o n d e r G r 6 s s e n o r d n u n g ~o -7 c,n. Z u f i i g u n g p o l a r e r S , , b s t a n z e n zu dem Ol h a t eine V e r / i n d e r u n g der Z~higkeit in der N ~ h e der W a n d zur Folge. [n einer Reihe yon F/illen vergmdert sich die ZS-higkeit s p r u n g w e i s e u n d z w a r bei einem A b s t a n d yon der \Vand yon der Gr6ss e n o r d n u n g x o - * - - [ o -5 cm. FOr polare Fliissigkeiten k a n n ,lie Z/ihigkeit abh/i.ngig yon der S t r u k t u r y o n Molekiilen. e n t w e d c r z u n e h m e n o d e r abnehmc,~ V e r s u c h s e r g e b n i s s e zeigen, class eine feste W a n d die O r i e n t i e r u n g der Molekiile y o n Fliissigkeitss c h i c h t e n bis a u f einen A b s t a n d yon [o -s c m u n d fiir p o l y m c r c l:liissigkeiten s o g a r his auf 1 e - a r m b e e i n f l u s s e n kann. Diese E r s c h e i n u n g s p i e l t e i n c b e d e u t e n d e l~olle in d c m .Mechanismus der Grenzs c h m i e r u n g denn. w e n n sie n i c h t a u f t r i t t v e r s c h w i n d e t auch relzehn~L~sig die %chliipfrigkeit.

Reference~ p. 294-295

282

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3

283

Zum Schluss wird die Frage d e r rnechanischen E i g e n s c h a f t e n der Grenzschichten yon Fliissigkeiten besprochen, m i t deren Hilfe sowohl die E x i s t e n z d e r statischen Reibung als auch die Giiltigkeit des binomialen Reibungsgesetzes, das DERYAGOI~" aus der rnolekul~ren Theorie der Reibung ableitete, erkl~.rt wurden. Als allgerneines Ergebnis tier U n t e r s u c h u n g e n wird festgestellt: Die Erscheinung der Grenzschmierung sind n i c h t zu erkliiren ohne die spezifische E i g e n s c h a f t e n der polymolekularen Grenzschichten yon Fliissigkeiten in B e t r a c h t zu ziehen.

INTRODUCTION

The far greater complexity of the phenomena of boundary friction as compared with fluid friction is clue to the fact that the former is in the main affected by the molecular interaction between the solid surfaces and the b o u n d a r y lubricating fihn in contact with them. an interaction which modifies the properties of the film. This is the dominant factor in the case of friction when the lubricating film is thin, whereas viscosity which alone determines the phenomena of fluid friction is of lesser importance at the small velocities at which boundary friction, and especially, static friction, usually takes place. Since experimental investigation of the properties of the boundary lubricating film is very difficult, the mechanism of b o u n d a r y lubrication has been insufficiently studied up to now. At present there are two opposing views on the mechanism of bounda~, lubrication. The first, worked out indetail by BOWDr:Nt, proceeds from the assumption that boundary friction is noticeably affected only by the properties of the friction surfaces themselves or of the monomolecular layers adsorbed on them. The layers of the lubricating substance beyond the first molecular layer are in a state so close to the volume state that they cannot exercise any specific influence on the phenomena of boundary lubrication, and therefore their properties are not i m p o r t a n t in this respect. A different point of view has been expressed by the authors of the present paper 2, and by a number of other Soviet scientists 3. According to their conception, based on a n u m b e r of experiments carried out mostly by new and original methods, the influence of the solid wall extends through many molecular layers of a liquid containing polar molecules, producing changes in their properties (as compared with those of the bulk phase) that have a considerable effect on the mechanism of lubrication. The time is now ripe to summarize the experimental data, which show that in the above-mentioned divergence of views preference must be given to the conception of long-distance surface action. A comprehensive survey should include investigations of the most varied effects for different liquids. As such surveys have already been publishedLS. particularly as regards the application of an analogous conception to the theory of the stability of colloids, worked out b y the author6, ~ as well as by VERWEY AND OVERBEEK s, GLAZMAN AND D Y K M A N ' and others, we shall confine ourselves to data directly concerning such behaviour and properties of boundary oil fihns as are closely related to their lubricating action (oiliness). References p. 294-295

284 A STUDY

B.V. Dedaguin OF VISCOSITV

IN T H I N

BOUNDARY

FILMS OF LUBRICATING

O I L S AND O T H E R

ORGANIC LIQUIDS

One of the methods of establishing the specific properties of b o u n d a r y films is to measure their viscosity. However, owing to the considerable e x p e r i m e n t a l difficulties involved, the majority of the previous studies either have been erroneous or have not reached clear and comprehensive conclusions. Special attention is d e s e r v e d by the work of BASTOW AND BOWDEN1°, who, in o r d e r to determine the viscosity, studied the radial flow in a narrow slit between parallel planes. They based their conclusion on a comparison of direct (optical) d e t e r m i n a t i o n of the gap-width between the plane with the value obtained from the measured resistance to flow of the liquid in the slit and the value of its b u l k viscosity. The c o m p u t e d width proved to be on an a v e r a g e o. I-O.2/z less than that obtained by light interference. As the average error in the determination of the width of the slit was of the s a m e o r d e r of magnitude, BASTOW AND BOWDEN concluded that their experiments c o n t r a d i c t the measurements that point to changes in the viscosity of the same liquids at a distance of over o.2 # from a solid wall. One could agree with the authors if t h e y h a d confined themselves to the a b o v e conclusion. However, they assumed without sufficient grounds that changes in viscosity also do not take place in thinner liquid layers adjacent to walls. Yet their experiments allow of an opposite interpretation. 1)espite the arbitrary extrapolation of the results obtained, BOWDEN based his further investigations of boundary lubrication o n the denial of the existence of peculiar w o p e r t i e s in the wall-adjacent liquid layers at a distance of less t h a n o.i u. Returning to the same subject in l~is work on the polymolecnlar adsorption of vapours on s m o o t h surfaces, 13OWD>;y tried to confirm his point of view. However, in this p a p e r u too, BOWDEN'S conclusions c o n s t i t u t e an ungrounded e x t r a p o l a t i o n of the experimental data, which in themselves arc not suitable for an estimation of the range oi surface action, inasmuch as ti',c ~n\.cstigation of vapour adsorption \\,as carried out only up to the relative pressure of o.95. I t is not surprising, therefore, t h a t the investigations of vapour adsorption in the i m m e d i a t e proximity of the s a t u r a t i o n point performed b y ZORIy AND DERYAGUIN I~, using an optical method, led to opposite results and conclusions. We shall now consider the results of direct measurements of viscosity in b o u n d a r y layers of organic liquids, oils and p o l y m e r s , performed by a precise a n d completely original method. These results point indisputal)ly to the fact t h a t in the boundary layers of up to o . I / z (and more, in some cases) the viscosity has a \-alue differing from that in the bulk.

MEASUREMENT

OF

VISCOSITY

IN

BOUNDARY

L\VERS

BY T H E

"BI.OW-OFF" M E T H O D

q'he shortcoming of all the methods h i t h e r t o employed in the investigation ol x iscos ity in thin films lies in the circumstance t h a t these methods, even if we disregard their other defects and sources of error, yield o n l y average effective vai'ues of the viscosity in the slit or in a layer of given thickness a~. Some methods, as for instance thost: based References p. 294-295

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285

on the flow of a liquid through porous m e d i a ~4, yield results that are even less definite, since the liquid passes through irregularly shaped pores for which the thickness of the layers is completely indeterminable. The "blow-off" method devised b y the authorstL I~ permits an exact determination of viscosity as a function of the distance from the solid wall, the latter being determined to within -t- 5 A. E X P E R I M E N T A L METHOD

One of the sides of a plane-parallel slit o.2 m m wide (Fig. I) was covered with a film of the liquid under investigation o v e r IO it thick. A constant stream of air blown through the slit produced a laminar flow in t h e film, giving it a gently sloping wedge-shaped form. Owing to the fact t h a t the flow of the film was caused solely by the shearing stress of.the air stream, which was u n i f o r m l y distributed over the whole surface of the fihn, the flow was one-dimensional as well as laminar. In other words, the velocity of the liquid Particles depended exclusively on the distance from the solid wall (z) but not on a n y other coordinates. T h u s t h e flow in the liquid layer was similar to that in a sheared deck of ordinary playing cards. An elementary layer of the liquid, parallel to the slit wall, moved as a whole parallel to the wall with a velocity u = u (z), increasing according to a definite function of the distance to the wall. This result is caused b y the fact t h a t , owing to the absence of volume forces, the state of stress in the film is homogeneous, and therefore the shear stress is the same at all points. If the viscosity were the s a m e at all distances from the solid wall too, then it would follow that the velocity g r a d i e n t bufi)z would also be eve~:where the same, and u, would be proportional to z. In this case the film would assume the shape of the exact wedge bounded on top by an inclined plane ; and vice versa, any variation in the value of the viscosity on approaching the wall would bring about a deviation from the strictly wedge-shaped form of the film, Thus we can judge the variations of viscosity near the solid wall from the profile of the film obtained after blowing-off. In fact, the resulting film profile represents on a definite scale the velocity profile of the liquid near the solid \~'all.

////////////////////////// Y///

.( Fig. t. S c h e m e of blow-off m e t h o d .

As proof of this, it is sufficient to p o i n t out t h a t if we place the origin of the coordinates (0) on tile wetting p e r i m e t e r (Fig. I) with the axis OX directed along the wall, and the axis OZ perpendicular to it, t h e n the abscissa x of a point of the film profile, situated at a distance h from the wall, expresses the distance travelled by the correReferences p. 294-295

286

B. V. Derjaguin

sponding elementary layer of the liquid during the blowing-off time z. But the distance travelled is proportional to the velocity: x -- *.~r: from which follows that the profile of the film represents the velocity profile in the liquid layers near the solid wall. Applying Newton's law of viscosity, we find the following formula for the viscosity of the liquid at a distance h from the wall: dh q = T r d.~"

(' )

The right-hand part of tim formula contains tile steepness d h / d x of the film profile at the spot where the thickness is equal to h. 7" denotes the shear stress in the layer of liquid, caused by the airflow. By determining the film profile obtained after blowingoff, we can establish the law of variation of viscosity as a function of the distance from the solid wall. Thus our main problem is to determine e x a c t l y the profile of a very thin film in the interval of thickness in which the variation in viscosity takes place under the influence of the solid wall. Depending on the nature of the liquid and the solid wall, the corresponding layer thickness may v a r y greatly in order of magnitude. In p o l y m e r liquids and solutions, variations of \iscosity lnav extend to distances up to 7-8 J~ from the wall. For monomei substances and common oils the layer is much thinner: a b o u t IO -s cm. Hence, the optical methods chosen to measure the thickness and profile of the film will vary greatly depending on the obiect under investigation_ In the first case a fairly accurate estimate of the velocity profile and the distribution of viscosity near the wall may be obtained by photographing the interference fringes of equal thickness, obtained by viewing the fihn in m o n o c h r o m a t i c light 1~ (see below). A far more sensitive and precise method is necessary in measuring the film thickness in common liquids and oils. \Ve chose a metlaod based on the determination of the parameters of the elliptical p¢,larizittio~t of the light reflected from various regions of the film. The necessit\, for determining the thickness in various regions of a film of unequal thickness made it impossible to apply the usual polarization goniometers and methods of observation requiring wide beams. The narrowing of the incident beam leads to a lowering in the intensity of the reflected light, which made the accurate deterruination of its state of polarization impossible. This difficult problem has been successfully solved by m e a n s of a special modulation method of analysis of the reflected polarized light, using a photoelectronic multiplier and an oscillograph. As a detailed description can be found in the original paper ~6, we shall confine ourselves to describing the scheme of the set-up (Fig. 2) and the method of measurement. The slit (A), illuminated by a tlg lamp, under 12o V a.c. with a light filter (F2) isolating the line 2. -= 5769-579 o A, was projected into the fihn under investigation, b y means of an object-lens (L) ; a, aperture d i a p h r a g m ; P,, iodine-quinine polaroid, on the measuring limb; P2, polaroid set in rotation around the reflected beam as an axis with a frequency of a b o u t t rev/sec. The modulated light fell on the photoelectronic multiplier, the voltage on which was increased by an amplifier with an RC References p. 294-295

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Fig. 2. Optical arrangement for determining velocity profile.

filter and t r a n s m i t t e d to the cathode oscillograph O serving as an indicator of the presence or absence of the modulation in the photocurrent. K x and K , are two q u a r t e r - w a v e plates: the principal axes of K~ are directed at an angle of 45 ° to the plane of incidence, the plate K , can be rotated and is on the measuring limb. Dx an Dp are two thick calcite plates cut not quite parallel to the optical axis; Dp serves to depolarize the b e a m in order to eliminate the influence of the sensitivity of the p h o t o c a t h o d e to the direction of polarization ; DK, the "decoherenter", serves to eliminate the coherence of ~:! and _[_ c o m p o n e n t s of the beam. With the decoherenter DK ill the " i n " position to prevent modulation, it is necessary and sufficient to r o t a t e the polarizer P~ to such a position that the I I and ± components of the reflected b e a m become equal. With the decoherenter in the " o u t " position to prevent a renewed modulation of the photocurrent it is necessary and sufficient to orient the optical axes or the plate Ks, which serves as an analyzer, so that they make an angle of 45 ° with the plane of polarization of the light transmitted by plate Kt. Ca]culations are m a d e in the usual m a n n e r with the azimuths obtained ~6. The technique of measuring was as follows. When the film on the surface o'f the steel plate had been blown off by an air current during time r, the a p p a r a t u s was demounted, the plate with the film was set on a micrometer slide, and by moving the latter the film thickness in various regions was measured. After that, a g r a p h was plotted representing the film profile. As the films of some liquids and solution were not very stable and evinced a tendency to disintegrate into drops, a different procedure was applied in this case. Tl,e thickness was measured not after but during blowing-off at a definite distance x 0 from the wetting line. For that purpose the c h a m b e r lid was m a d e transparent. For rapid optical measurements the following modification of the tecl',nique was particularly convenient. The oil film was s m e a r e d on the underside of a glass prism that served as a lid for the blowing-off chamber, the angle of incidence of the polarized light being 45 ° ; complete internal reflection was thus observed; the a m p l i t u d e s of the component oscillations parallel and normal to the plane of incidence remained constant, but a phase shift appeared. In the presence of the film this shift varied, depending on the thickness of the film. The a d v a n t a g e of the a b o v e - m e n t i o n e d technique lies in the fact that only one azimuth needs to be measured, instead of two. By plotting tile thickness of the film h against the value U =: xo/r the results of the measurement m a d e according to the second v a r i a n t were brought to a form representing References p. 294-295

288

B. V. Derjaguin

t h e film v e l o c i t y profile in t h e p r o x i m i t y of t h e s o l i d w a l l as was d o n e in the first v a r i a n t (r is t h e p e r i o d of t i m e from t h e b e g i n n i n g of b l o w i n g - o f f to t h e m o m e n t of m e a s u r i n g ; h is t h e t h i c k n e s s m e a s u r e d a t t h a t m o m e n t ) . O b v i o u s l y the a b s c i s s a expresses t h e v e l o c i t y of the l a y e r s a t a d i s t a n c e h f r o m t h e wall. T h u s t h e g r a p h gives the v e l o c i t y profile. I t s x 0 was d i f f i c u l t to d e t e r m i n e ; we u s u a l l y p l o t t e d z / T o n the axis of the abscissa, w h i c h r e s u l t e d in t h e s a m e v e l o c i t y profile b u t on a n a r b i t r a r y scale. Figs. 3, 4, 5, 6 a n d 7 show the r e s u l t s o b t a i n e d b y V. V. KARaSSEV; F i g s . 3 a n d 5 were o b t a i n e d b y t h e first m e t h o d , t h e r e s t b y t h e second. RESULTS OF THE MEASUREMENTS Fig. 3 refers to n o n - p o l a r v a s e l i n e oil ; t h e p o l a r i m p u r i t i e s were r e m o v e d b y a special p r o c e d u r e w o r k e d o u t b y P r o f e s s o r ELOvm~t, i n v o h , ing t h e use of a p l a t i n u m c a t a l y s t a t high t e m p e r a t u r e .

y(£)

2000 200C

1600

soo

12OO 800

iooo 50o o

400 1 2 3 4 5 6 7 8

¢m

t'- 104 I/T ~

Fig. 3- Velocity profile for specially purified vaseline oil on a steel surface, obtained by analysis of fihn profile after blowing i = 2o°C.

~

3,

Vr

Fig. 4- \;elocity profiles of o.o1°/o solutions of chlorine derivatives of tetracosane in vaseline oil, on a steel surface, obtained in the process of blowing. ( [ ) Monochlorotetracosane solution, t = ~3°C ; (2) Trichtorotetracosane solution, t = i8 6°C; (3) Hexachlorotetracosane solution, t = :5"C.

W e see t h a t t h e v i s c o s i t y of n o n - p o l a r v a s e l i n e oil r e m a i n s a c o n s t a n t v a l u e equal to its value in the b u l k up to a d i s t a n c e of a b o u t [o -7 c m from the wall. S i m i l a r results h a v e been o b t a i n e d dozens of times, w h i c h p r o v e s t h e m to be correct b e y o n d a n y r e a s o n a b l e d o u b t . N e v e r t h e l e s s , t h e a d d i t i o n of f a t t y a c i d s or e t h e r s in m i n u t e concent r a t i o n s can d i s t u r b the l i n e a r i t y of tim v e l o c i t y profiles. \ V i t h an increase in concent r a t i o n t h e film profile b e c o m e s i r r e g u l a r a n d j a g g e d , while a still g r e a t e r i n c r e a s e of the c o n c e n t r a t i o n m a k e s t h e film u n s t a b l e : it no l o n g e r w e t s the surface, which is c o v e r e d w i t h an a d s o r b e d film of a s u r f a c e - a c t i v e s u b s t a n c e . Fig. 4 r e p r e s e n t s the v e l o c i t y profile w h e n a m o n o c h l o r o p a r a f f i n , t r i c h l o r o p a r a f f i n or h e x a c h l o r o p a r a f f i n a r e a d d e d to t h e vaseline oil in a c o n c e n t r a t i o n of o.o~ %. In this case the form of the profile c h a n g e s a n d a s s u m e s a c h a r a c t e r i s t i c b r e a k of a b o u t o.o2 5 F i n t h i c k n e s s . S i m i l a r results are o b t a i n e d in the case of s o m e p o l a r s u b s t a n c e s in t h e pure form (see Fig. 5)In some cases, as for i n s t a n c e for i n c o m p l e t e l y h y d r a t e d b e n z a n t h r o n e (Fig. 6), the profile o b t a i n e d r e v e a l s lower v i s c o s i t y n e a r t h e wall, which is p r e s u m a b l y c o n n e c t e d References p. 294-295

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289

with the ring structure of the molecules. This structure enables the molecules to become orientated horizontally near the wall, and this leads to a lowering of viscosity.

y(~,) 10o0

8oo

soo

40

v

v

l/r

Fig. 5- Velocity profiles of esters on the surface of steel, obtained by analysis of film profiles after blowing. (t) Amyl sebacate ; (2) Dibutyl phthalate.

=-I/r Fig. 6. Velocity profiles of incompletely hydrogenated benzanthrone on a glass surface, obtained during blowing.

DISCUSSION Inasmuch as viscosity is a structure-sensitive property the results obtained reveal that structural peculiarities occur, in the boundary layers of a liquid in which polar molecules are present in the minutest concentration. The fact that the structure is affected by minute concentration of surface-active substances indicates that the action of the latter cannot be due to their presence throughout the fihn, but is connected with the formation of a definite monolayer. The appearance of sudden changes in the viscosity, and hence also in the structure at distances up to o. z #, proves that theorientated monolayer is in some way able to affect the orientation of adjacent molecules of the non-polar solvent, and that this influence extends throughout hundreds of molecular layers. Tkis conclusion is particularly supported by the results (Fig. 4) of the experiment with solutions of chlorol)araffins in vaseline oil. The jagged curves representing the velocity profile point to the fact that the structure of the boundary layers of liquids can change abruptly at a certain distance from the solid wall; this confirms the concIusion made previously in the case of measurement of the adsorption of vapours of volatile liquids near the saturation point. The results obtained for fatty acid and ether (Fig. 7) solutions in vaseline oil are rather complicated and deserve special consideration. In the case of weak concentration of surface-active molecules the velocity profile assumes a rather irregular shape, which evidently points to the structural heterogeneity of the corresponding layers of the solvent. This heterogeneity can be explained b y the circumstance that different s t r u c References p. 294-295

290

B.V. Derjaguin y(X) 1500 1000 5O0

Fig. 7. V e l o c i t y p r o f i l e s of s o l u t i o n s of s t e a r i c a c i d a n d a m y l s e b a c a t e o n a g l a s s s u r f a c e d u r i n g blowing. (I) o . o o o o z i 30 s t e a r i c a c i d ; l = IS°C. (3) o - o o 2 5 c}~ a m y l s e b a c a t e ; t - I8°C. (2) 0 . 0 0 0 5 4 °,o s t e a r i c a c i d ; l -- i4"(;. (,t) o . o o 6 o o~ a m y l s e b a c a t e ; t = 18°C.

tures of the wall-adjacent layer of the solution are possible, depending on the orientation of the adsorbed molecules, which in turn m a y v a r y over the surface. In a number of cases, if the layer is left undisturbed, we failed to observe any furthcr appearance of irregularities in the profile, and in fact the existing ones were smoothed out. It follows that the film profile obtained after blowing-off assumes its jagged shape as a result of deformation during laminar flow and not because of its thermodynamic instability. The effect is similar to that of the formation of slip bands in plastic deforntatioM 8 and points also to tile heterogeneous structure of the boundary layer. At the same time the fluidity preserved by the b o u n d a r y layer even under the small sheai stress caused by the air s t r e a m shows that the mechanical properties of a liquid layer differ greatly from those of a plastic solid body, although there are apparently some exceptions to this rule; moreover, the resistance of the b o u n d a r y layer to thinning points to tile difference between its properties and those of the bulk liquid. It m a y be supposed t h a t tlm b o u n d a r y lubrication laver is in a state siinilar to thal of liquid crystals with a s t r u c t u r e in which the nmin part is played by the orientatio,: of rod-shaped molecules. y(X}¢ 40 000/

ooool ~ 0 0 0 0 ~ K'V~c

t

g

±_

0.5

1.0

1.5

I __~- 103 [/r

0

2.0

csn sec

l"ig. 9 k " e h ) c i t y p r o I i l c Oll s t e e l s t u l a c c for v i n y l b u t y l e t h e r p o l y m e r . ~I = 600; r : 48 r a i n ; AP : :;o m m H g ; l = ~o~(; C? = looC~.

I"ig. 8. l ' h o t o g r a p h of t h c i n t e r f e r e n c e p a t t e r n [ o l n l c d Oll a s t e e l s u r f a c e w h e n b l o w i n g off a p o l y m e r of v i n y l b u t y l e t h e r . 31 ~ 6 o o ; 1" = 48 r l u n ; L~P = 20 n u n H g ; t -:- 2 o ' ~ ; C -= I o o % ( 3 t is m o l e c u l a i w e i g h t , r is b k , w i n g - ( ~ f f t i m e , A 1 ~ is p r e s s u r e d r o p . ! is t e m p e r a t m e , C is c o n c e n t r a t i o n ) . T h e d i r e c t i o n of t h e a i r j e t : ;

References p. 294-295

Selected Works - 3

291

Tile chief difference from liquid crystals is that in the latter the solid wall causes an orientation spreading at an indefinite distance, while with liquids the distance is quite definite and small. The intermediate case m a y include some liquids and solutions containing polymers. As we have already shown, in this case, one can get an idea of the viscosity distribution in the proximity of the solid wall from the position of the interference flinges of equal thickness. Fig. 8 is a photograph of poly (vinyl butyl ether) with a molecular weight 6oo, which was kindly supplied by Professor M. F. SHESTAKOVSI(Y.The greater density of the fringes in the thin part of the layer points to an increase of the viscosity there. An analysis of the photograph yields the velocity profile of the film on the solid wall, represented graphically in Fig. 9The complex phenomena of viscosity changes and tim appearance of zones of unstable thickness are observed upon the addition of various vinyl polymers to mineral oils. Since they are described in detail in original papers *~ we shall confine ourselves to showing photographs (Figs. IO and IZ) representing two typical cases.

J

tl

;

F i g . io. P h o t o g r a p h o f i n t e r f e r e n c e p a t t e r n formed on a steel surface when blowing-off a p o l y m e r solution of v i n y l b u t y l e t h e r in t u r b i n e oil. M = - ' , l o o : r = i 2 r a i n ; / 5 1 ~ = 2o m m H g ; t = zoCC; C -= o.o40/~).

•

.

,<

F i g . I i . P h o t o g r a p h of i n t e r f e r e n c e p a t t e r n f o r m e d on a steel surface w h e n b l o w i n g - o f f a p o l y m e r s o l u t i o n of v i n y l l m t y l e t h e r in t u r b i n e oil. 214- = 3 , 8 5 o ; r -- 3 r a i n : A ] ) = 7 o m m H g ; t 2 o ° C ; C = o o 3/o" -°/

T I l E N A T U R E OF S T A T I C F R I C T I O N I N B O U N D A R Y L U B R I C A T I O N T H E T W O - T E R M L A W OF FRICTION

The results obtained indicate tile peculiarities in tile structure and fluidity of the boundary layers of lubricating liquids and hence lead us to conclude that these peeuReferences p. 294-295

292

B.V. Derjaguin

liarities lnust be taken into consideration in interpreting the phenomena of boundary lubrication and in working out their theory. Owing to lack of space we shall not dwell on these questions, especially since the results of the investigations - in particular those concerning static and kinetic disjoining pressure in thin liquid films ~9, the kinetics of the thinning of b o u n d a r y layers between two solid bodies in contact with one another 20, the interrelation of kinetic friction and molecular orientation ~, etc. - are discussed in a number of other papers. We shall limit ourselves to a consideration of the following important problem. If the boundary lubrication layer does not possess a yield value, as is indicated by the results of application of the blowing-off method, then how can one explain static friction between solid surfaces, separated b y a polymolecular layer? Yet, the existence of static friction in such cases has been convincingly proven in a number of experimental studies 2z. We believe that the correct answer to the question can be found only in the two-term friction law previously formulated by us 2a and experimentally proved 24. The validity of this law for the interpretation of the mechanical properties of liquid and solid lubricating films has been proved in the work of DERVAGUI~ AND LAZARF.V2s. According to the two term law of friction, the force of static friction F equals :

F = t ~ (N q- Sp,) = t z N

+ SO

( 0 - / ~ p.) ,

where # is the " t r u e " coefficiet~t of friction, N the load, oc the area of real or molecular contact, and P0 the adhesion force per unit area of real or molecular contact. This fommla, which in form but not in physical content is to some extent analogous to the two-term Coulomb Law (deduced empirically), expresses the idea of the double oi igin of the force of friction. Ore: part of this force is caused by exterual pressure N, the other part by the molecular interaction of the surfaces. The law also reflects the divergence between the views of the present authors and BOWDEN, who interprets the friction phenomena ~ by means of the second term of the formula alone, which amounts to the assumption that the "true" coefficient of friction/x equals zero. Tllus, according to t~owm-x and his school, friction depends on the load N only insofar as the latter increases the area .5 of true or n:olecular contact between the bodies. This point of view, first forlnulated by "FERZA~R126, is in contradiction with experiments in which the force of friction increases with the load in strict accordance with the linear law, despite the fact that either the area of molecular contact cannot undergo essential changes 2s o~ that this increase in the area is slower than that of ti,e toad zT. To this end we investigated the [fiction of a plane paraffin block on glass. In order to obtain a large area of contact that was not changed throughout the experiment, the paraffin was preliminarily melted while in contact with the glass surface and then allowed to solidify, tn order to be certain that sliding took place not between the layers of paraffin, but on the paraffin-glass interface, the latter was covered with a multiReferences p. 294-295

Selected Works

3

-

293

molecular layer of the acid b a r i u m or calcium salt of stearic acid, according to the m e t h o d of BLODGETT AND LANGMIJIR. The n u m b e r of layers n varied from 1-61. Figs. I2 and 13 represent the observed dependence of the force of friction on the load. This dependence bears out the correctness of our t w o - t e r m law of friction. The circumstance that the angle of inclination of the straight lines, which is equal to the true coefficient of friction, is independent of the n u m b e r of molecular layers n proves that the macroscopical asperities of the glass surface have very little influence on the coefficient of friction.

I

F

x1

2O0

200

I

i

200

..---qr

400

0

200

400

Fig. i2. F r i c t i o n force p l o t t e d a g a i n s t load for p a r a f f i n o n glass. L u b r i c a n t : m u l t i m o l e c u l a r B l o d g e t t - L a n g m u i r l a y e r s of acid calc i u m s o a p w i t h n molecular layers. O, }'l = I; o, ~/ = 3; x , l l = 3 t ; , t , n = 6t.

_

2~

600 N

I

-

0

_.

2~

t

1

4~

6~

N

Fig. t 3- Friction force plotted against load for p a r a f f i n on glass. L u b r i c a n t : m u l t i m o l e c u l a r B l o d g e t t - L a n g m u i r layers of b a r i u m s o a p w i t h n molecular layers. O.

u

:

3:o,n

=

7;

X.n

=

21.

The second term in the linear taw, according to the above data, declines somewhat as the n u m b e r of layers n increases from 7 to 9, and remains constant with further increase of n. This decrease in the value of the second term with increasing thickness of the lubricating layer can be easily explained, according to P. A. R E H B I N D E R , bv assuming t h a t in thicker lubricating layers tile molecular attraction between the glass and the paraffin ceases to h a v e effect, while the adhesive force N depends only on the interaction between the molecules of the lubricant and the paraffin. Another m e t h o d of refuting the o n e - t e n n law and proving the two-term law of friction consists in studying the influence on friction of a variation m the deformability of the areas of contact, with the n a t u r e of the surfaces and the conditions of measurement remaining the same. This idea was tested b y U. TOPOROFF ill our laboratory. He compared the friction between a m e t a l surface and a glass point with radius of curvature of about I / I o m,n in one case, and between a m e t a l surface a n d a thin-walled glass ball with radius of curvature equal to several centimeters. The coefficient of friction on the unlubricated metal was always greater in the second case than in the first. But when the metal surface was covered by an adsorbed m o n o l a y e r of stearic acid this difference disappeared. This experiment furnishes proof of the correctness of the two-term law of friction. In the case of a thick layer of b o u n d a r y lubricant, we liave the reverse case, when the second t e r m is equal to zero. In fact, in the case of boundary lubrication the second References p. 294-295

294

B.V. Derjaguin

t e r m , if r e f e r r e d t o u n i t a r e a , s h o u l d e x p r e s s t h e y i e l d v a l u e 69, w h i c h in a c e r t a i n n u m b e r of cases o f b o u n d a r y l u b r i c a t i o n e q u a l s z e r o , a s is d e m o n s t r a t e d

by the results

o b t a i n e d b y t h e b l o w i n g - o f f m e t h o d . A c c o r d i n g t o c u r r e n t v i e w s *~ in t h a t case, s t a t i c f r i c t i o n s h o u l d b e e x a c t l y z e r o . F r o m o u r p o i n t of v i e w , h o w e v e r , we m u s t t a k e i n t o c o n s i d e r a t i o n t h e first t e r m , w h i c h n o t o n l y e x p l a i n s t h e p r e s e n c e of s t a t i c f r i c t i o n , b u t also p r o v i d e s a basis, in a c c o r d a n c e w i t h t h e e x p e r i m e n t s , for t h e o n e - t e r m f r i c t i o n l a w of At~ONTON, w h i c h is s t r i c t l y v a l i d in c a s e s o f b o u n d a r y

lubrication.

T h e a b o v e c o n s i d e r a t i o n s a r e , of c o u r s e , s o m e t h i n g m o r e t h a n a f o r m a l d e d u c t i o n f r o m t h e o b s e r v e d p h e n o m e n a . T h e c o n c l u s i o n d r a w n , t h o u g h e m p i r i c in origin, c o n t a i n s a n essentially new a s s u m p t i o n t h a t deserves f u r t h e r i n v e s t i g a t i o n and proof: viz. that r e s i s t a n c e to s h e a r in a t h i n b o u n d a r y

l u b r i c a t i n g f i l m is b r o u g h t a b o u t b y a n o r m a l

l o a d on the film, a n d a p p e a r s a n d d i s a p p e a r s w i t h t h e load. L a c k of s p a c e d o e s n o t a l l o w us to p r e s e n t f u r t h e r e v i d e n c e of t h i s i m p o r t a n t f u r n i s h e s the o n l y e x p l a n a t i o n of t h e m e c h a n i s m

p r i n c i p l e , w h i c h , in o u r o p i n i o n ,

of b o u n d a r y

lubrication consistent

w i t h all the e x p e r i m e n t a l d a t a .

RE FERE,\:CES t I7. p. BOWDEN AND D TABOR, The ffriclton a~*d Lubricalion o[ Solids, 2nd ed., Oxford Unix'.

Press. l.ondon. 1954.

2 g . V I)ERVAGUIN, N . N. ZAKHAVAEVA, ~'1. 1~{. I(USSAKOV,

.-tkad ha,.~" S . S . S . R . , T r u d y I Vsesoyuz N o n /

V. P. LAZAREV AND ~[. ~ . SA.M~t'GUIN,

T r e n i y u i I z n o s u . l I a s h i n a M ~ . z (1947) [o3-I39;

3 (1949) lOt 13. V. D E R v . ~ o t ; I . ~ , C h t a T a k o y e T r e n D ' e ? ( \ V h a t i s f r i c t i o n ? ) Acad. Sci. U.S.S.I~-., 193~, (in t{ussian) a ..\ S. AKH>-I.a.TOV,Trudy z Vsesoyuz. K o n / . T r e n i y u 1 lz~msu k'[ashinakh, 3 (1949) 133, I44 a j. c HE>:
:ltashi-

n o w d e n i v a . Sootschanie. po I.'iazkosli Zhidkosl. i Nolloid. Rastvorov, z (194 ~) 59. t~ B. V. DE~Y.~,GUIN AND N A. I(RYLOV, A k a d . N a u k . S . S . S . R . , O t d t l . Tekh. N a u k . , l n s t Mashinovede.niva. Soveschanie po V i a z k o s t i Zhidkost. i Kolloid. Rastvorov, z (~944) 52. ts B. V. DkRVa.GUtN. G. 31. STRAKHOVSKI AND D. S. ){XLYSHEVA, Z h u r . Eksptl. i Teorct. Fie., _r6 (1946) t71: A c t a Pha,sicochim. U . R . S . S . , 29 (1944) 54 tB. V. DERV.*,GUINAND I~. F. P l c l l o G u I N , A k a d . N a u k . S . S . S . R . , T r u d y z Vsesoyuz. Kon[. T r e n u u i Iznosu :IIashinakh, z (~947) t o 3 ; 3 (1949) [ o r . is 13. \:. DEItVXGUI.~ AND \-. V. KARASSEV, D o k l a d y .4kad. N a u k . S . S . S . R . , 62 (1948) 761 : ffolloid Zhur., 15 (1953) 365: Doklady A k a d . N a u k . S . S . S . R . , z o x (1955) 289. 17 B. V. DERV.a,GUIN ~ND .",'. N. ZAKHAV.a,EV.',, T r u d y 1(o,1. po l l y s o k o " tolekular- Soedi~e~tij,am. A k a d . N a u k . S . S . S . R . Otdel. K h i m . i Fiz. M a t . - N a u k , 6lh Con[. 2949, P- 233 ts N. F. SJt:rr,:tg, D o k l a d v .4kad. N a u k 5.5; S . R . , 9 6 ( 1 9 5 4 ) 5 0 3

Selected Works

-

3

19 ]3. V. DERYAGUIN AND E. V. OBUKHOV, Kolloid. Zhur., I (t935) 385; Acta Physicochim. U.R.5.S., 5 (t936) t. ]3. V. DERYAGUIN AND ~1. ~{. KUSSAKOV,lzvest. A k a d . Nauk, S.S.S.R., Set. K h i m . , 5 (I937) I I I9; A cla Physicochim. U.R.S.S., Io (1939) 25. x53 ; Trans. Faraday Soc.,36 (t94o) 203 ; Kolloid.Zhur., 6 (I94 o) 3 9 I . B. V. DERYAGUIN, M. J~I. [{USSAKOV AND L. S. LEBEDEVA, Doklady Akad. N a u k S.S.S.R., 23 (1939) 67 ° . ]3. V. DERYAGUIN, M. 31. I{USSAKOV AND A. S. TITIJEVSKAJA, Kolloid. Zhur,, 15 (t953) 4t6, to A . I). MALKINA AND B. V. DERYAGUIN, I(olloid. Zhur., I2 (t95o) 43 I. tt V. P. LAZAREV AND g . V. DERYAGUIN,Zhur. Tekh. Fiz., 23 (t953) 1977. Z2 n . V . DERYAGUIN, 1~. N. ZAKHAVAEVA, ]X]. M. KUSSAKOV, V. P. LAZAREV AND M. M. SAMYGUIN, Akad. N a u k . S.S.S.R., Trudy 2 Vsesoyuz. ](on/. T r e n i y u i Iznosu, 3 (t949) 144 ; Doklady Akad. N a u k . S.S.S.R., 3o (1941) xI9. t3 ]3. V. DERYAGUIN, Z. Physik, 88 (I934) 661 ; Zhur. Fiz. Khim., 5 (x934) I [65 24 B. V. DER','AGUIN, DoMady Akad. N a u k S.S.S.R., 3 (I934) 93B. V. DERYAGUIN AND V. P. LAZAREV, I(olloid. Zhur., I (1935) 293. ~ I~. V. DER~'AGOIN AND V. P. LAZAREV, ,4had. N a u h S.S.S.R., Trudy 2 Vsesoyuz. 1(on/. Treniyu i lznosu Mashinakh, 3 (1949) io6. =6 TERZAGm, Erdbaumechanik, Wien, 5 ° (I925) ; J. J. ]3~KERMAN AND E- K. RtDEAL, Phil. Mag., 27 (I939) 687; F. BOWDEN AND D. T.~,BOR. Proc. Roy. Soc. (London), A 169 (I939) 3 9 t 27 j . v . KRAGELSKX. Zhur. Tekh. Fiz.. x2 (t942) 7-"6. ~s \V. ]-lARDY, Proc. Roy Soc. (London), A ~o8 (I9-~5) 1.

295